We can solve this together! We're beginning with 189396 and removing 15581 from it.

Step 1: We'll start by subtracting the digit 1 and the borrow 0 from 6 in column 1 and get 5.
5 is the first digit of our result.

Step 2: We'll start by subtracting the digit 8 and the borrow 0 from 9 in column 2 and get 1.
1 is the next digit of our result.

Step 3: We'll start by subtracting the digit 5 and the borrow 0 from 3 in column 3 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 4: We'll start by subtracting the digit 5 and the borrow 1 from 9 in column 4 and get 3.
3 is the next digit of our result.

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 8 in column 5 and get 7.
7 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 1 in column 6 and get 1.
1 is the next digit of our result.

So, 189396 - 15581 = 173815.